On $\alpha$-almost Artinian type modules

نویسندگان

1 Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

doi
10.22034/as.2024.21355.1706
چکیده

In this article we introduce and study the concepts of $\alpha$-almost Artinian type and $\alpha $- Krull type modules. Using these concepts we extend some of the basic results of $\alpha $-almost Artinian and $\alpha $-Krull modules to $\alpha$-almost Artinian type and $\alpha $-Krull type modules. We observe that if $M$ is an $\alpha$-Krull type module then the uncountably generated Krull dimension of $M$ is either $\alpha$ or $\alpha+1$.